Multiple parameters in Python - Time & Space Complexity

Time Complexity: Multiple parameters

O(n * m)

Understanding Time Complexity

When a function takes more than one input, we want to know how its running time changes as these inputs grow.

We ask: How does the work increase when each input gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

def combine_lists(list1, list2):
    result = []
    for item1 in list1:
        for item2 in list2:
            result.append((item1, item2))
    return result

This function pairs every item from the first list with every item from the second list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Nested loops over both lists.
• How many times: Outer loop runs once per item in list1; inner loop runs once per item in list2 for each outer loop.

How Execution Grows With Input

Each item in the first list pairs with every item in the second list, so work grows with both sizes multiplied.

Input Size (list1, list2)	Approx. Operations
(10, 10)	100
(100, 100)	10,000
(1000, 1000)	1,000,000

Pattern observation: Doubling both lists multiplies work by four; work grows fast as both inputs grow.

Final Time Complexity

Time Complexity: O(n * m)

This means the time grows by multiplying the sizes of both inputs together.

Common Mistake

[X] Wrong: "The time depends only on the bigger list size."

[OK] Correct: Because the function pairs every item from one list with every item from the other, both sizes matter equally.

Interview Connect

Understanding how multiple inputs affect time helps you explain your code clearly and shows you can think about real problems with several factors.

Self-Check

"What if we changed the inner loop to only run half the size of list2? How would the time complexity change?"

Practice

1. What does it mean when a Python function has multiple parameters?
def greet(name, age):

easy

A. The function can only have one parameter at a time.

B. The function can only return multiple values.

C. The function must be called without any arguments.

D. The function can receive more than one piece of information to work with.

Solution

1. Step 1: Understand function parameters

   Parameters inside parentheses let a function accept inputs to use inside its code.

2. Step 2: Multiple parameters mean multiple inputs

   When separated by commas, each parameter is a separate input the function expects.

3. Final Answer:

   The function can receive more than one piece of information to work with. -> Option D

4. Quick Check:

   Multiple parameters = multiple inputs [OK]

Hint: Multiple parameters mean multiple inputs separated by commas [OK]

Common Mistakes:

• Thinking parameters are outputs
• Believing functions can't have more than one parameter
• Confusing parameters with function return values

2. Which of the following is the correct way to define a function with two parameters named x and y?

easy

A. def add(x; y):

B. def add(x y):

C. def add(x, y):

D. def add[x, y]:

Solution

1. Step 1: Check function definition syntax

   Python functions use parentheses to list parameters separated by commas.

2. Step 2: Identify correct separator and brackets

   Parameters must be separated by commas inside parentheses, not spaces, semicolons, or brackets.

3. Final Answer:

   def add(x, y): -> Option C

4. Quick Check:

   Parameters separated by commas inside () [OK]

Hint: Use commas between parameters inside parentheses [OK]

Common Mistakes:

• Using spaces instead of commas
• Using semicolons or brackets instead of commas and parentheses
• Missing parentheses around parameters

3. What will be the output of this code?

def multiply(a, b):
    return a * b

result = multiply(3, 4)
print(result)

medium

A. 12

B. 7

C. 34

D. Error

Solution

1. Step 1: Understand function call with parameters

   The function multiply receives 3 and 4 as inputs for a and b.

2. Step 2: Calculate the return value

   It returns the product 3 * 4 = 12, which is stored in result and printed.

3. Final Answer:

   12 -> Option A

4. Quick Check:

   3 times 4 equals 12 [OK]

Hint: Multiply inputs given to function parameters [OK]

Common Mistakes:

• Adding instead of multiplying
• Concatenating numbers as strings
• Expecting an error due to parameters

4. Find the error in this function definition:

def greet(name, age)
    print(f"Hello {name}, you are {age} years old.")

medium

A. Missing colon at the end of the function header.

B. Parameters should be inside square brackets.

C. The print statement should be outside the function.

D. Function name cannot be 'greet'.

Solution

1. Step 1: Check function header syntax

   Python requires a colon ':' at the end of the function header line.

2. Step 2: Identify missing colon

   The given function header lacks the colon after the closing parenthesis.

3. Final Answer:

   Missing colon at the end of the function header. -> Option A

4. Quick Check:

   Function header must end with ':' [OK]

Hint: Always put ':' after function header parentheses [OK]

Common Mistakes:

• Forgetting the colon ':'
• Using wrong brackets for parameters
• Misplacing print statement

5. You want to write a function describe_person that takes name, age, and city as parameters and returns a sentence like:
"Alice is 30 years old and lives in Paris."
Which function definition and return statement is correct?

hard

A. def describe_person(name, age, city):
print(f"{name} is {age} years old and lives in {city}.")

B. def describe_person(name, age, city):
return f"{name} is {age} years old and lives in {city}."

C. def describe_person(name, age, city):
return name + " is " + age + " years old and lives in " + city + "."

D. def describe_person(name, age, city):
return f"{name} is {age} years old lives in {city}."

Solution

1. Step 1: Check function parameters and string formatting

   The function must accept three parameters and return a formatted string with all parts included.

2. Step 2: Compare return statements

   def describe_person(name, age, city): return f"{name} is {age} years old and lives in {city}." uses an f-string correctly with all parts and punctuation. def describe_person(name, age, city): return name + " is " + age + " years old and lives in " + city + "." tries string addition but age is an int, causing error. def describe_person(name, age, city): print(f"{name} is {age} years old and lives in {city}.") prints instead of returning. def describe_person(name, age, city): return f"{name} is {age} years old lives in {city}." misses 'and' in the sentence.

3. Final Answer:

   def describe_person(name, age, city): return f"{name} is {age} years old and lives in {city}." -> Option B

4. Quick Check:

   Use f-string with all parameters and return [OK]

Hint: Use f-string with all parameters and return the string [OK]

Common Mistakes:

• Concatenating strings with int without conversion
• Using print instead of return
• Missing words or punctuation in the string